Weighted product Hardy space associated with operators

Abstract

Assuming that the operators L₁, L₂ are self-adjoint and {\mathrm{e}}^{-{{\displaystyle tL}}_i}(i=\mathrm{1},\mathrm{2}) satisfy the generalized Davies-Gaffney estimates, we shall prove that the weighted Hardy space {{\displaystyle H}}_{{{\displaystyle L}}_{\mathrm{1}},{{\displaystyle L}}_{\mathrm{2}},\omega }^{\mathrm{1}}({ℝ}^{{{\displaystyle n}}_{\mathrm{1}}}\times {ℝ}^{{{\displaystyle n}}_{\mathrm{2}}}) associated to operators L₁, L₂ on product domain, which is defined in terms of area function, has an atomic decomposition for some weight \omega.

Key words： Produce Hardy space; Ap weights; Davies-Ga_ney estimates

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